Gregory L. Naber Knihy

The book presents a mathematically rigorous exploration of special relativity while emphasizing the physical significance behind the mathematics. It covers traditional topics as well as contemporary results, including Zeeman's causal automorphisms, the Penrose theorem, and a detailed introduction to spinors. The second edition introduces a new chapter on the de Sitter universe, guiding readers into the complexities of gravitational fields and models of an expanding universe. The text is accessible, requiring only basic knowledge of linear algebra and real analysis.

Exploring the foundations of quantum mechanics, this work delves into the origins of the Planck constant and Heisenberg algebra, as well as Feynman's motivation for the path integral formulation. It distinguishes between bosons and fermions, providing a thorough mathematical treatment of these concepts. The inclusion of extensive Appendices and Remark sections enriches the reader's understanding, making complex ideas accessible while maintaining rigorous standards.

Focusing on the Yang-Mills field, this second edition explores the profound influence of mathematical physics, particularly gauge theory, on the geometry and topology of manifolds. It delves into the intricate relationship between these mathematical concepts and their applications, providing a comprehensive understanding of how they intersect and shape modern mathematical thought.

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.